The NT is supposed to have inclusivity as a value and they are trying to demonstrate that. As a member of the public what am I to make of visiting somewhere that has volunteers who aren't wearing the lanyards?
I would think nothing of it. I work at a professional organisation where many people wear their security badges on lanyards. You see pretty much every colour under the rainbow and, indeed, the rainbow.
This isn't 'poppybfacism' (I don't wear one because I don't represent any organisation so it's no-ones business). Volunteer or not, they are representing the NT and they do have to adopt a professional attitude that is in line with the organisation's aims. This isn't like running the local cats home.
The organisation's aims are to preserve some of our countryside and historic buildings. That doesn't preclude celebrating LBGT history, particularly this year, but that doesn't mean forcing people to wear a particular lanyard. You are not demonstrating solidarity with the gay community or inclusivity if you have to make it compulsory.
I'd be all for this right up to the moment when they say you
must do it. That's the moment when irony sets in.
As for the film, the gentleman is dead so I don't see it makes a lot of difference to him.
Did Robert Wyndham Ketton-Cremer ever express an opinion on whether he should be outed 48 years after his death in an era where attitudes to gay people are somewhat different to his own era? For almost his entire life it was illegal to be a homosexual. That seems to me to be motive enough to keep his sexuality secret. Perhaps today he'd be open about it and maybe happier.
Oh, and the family members objecting are his god children according to Wikipedia, so it is not obvious how close they were to him.